Answer :
To solve the equation [tex]\( 20x + 27(x - 4) = 221 \)[/tex], we can follow these steps:
1. Remove the parentheses:
- Distribute the 27 across the terms inside the parentheses:
[tex]\[
20x + 27(x - 4) = 20x + 27 \cdot x - 27 \cdot 4
\][/tex]
- Simplify:
[tex]\[
20x + 27x - 108 = 221
\][/tex]
2. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms on the left side:
[tex]\[
20x + 27x = 47x
\][/tex]
- This simplifies the equation to:
[tex]\[
47x - 108 = 221
\][/tex]
3. Isolate the variable ([tex]\( x \)[/tex]):
- Add 108 to both sides to get rid of the constant on the left:
[tex]\[
47x - 108 + 108 = 221 + 108
\][/tex]
- Simplify:
[tex]\[
47x = 329
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Divide both sides of the equation by 47 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{329}{47}
\][/tex]
- This gives:
[tex]\[
x = 7
\][/tex]
So, the solution to the equation is [tex]\( x = 7 \)[/tex].
1. Remove the parentheses:
- Distribute the 27 across the terms inside the parentheses:
[tex]\[
20x + 27(x - 4) = 20x + 27 \cdot x - 27 \cdot 4
\][/tex]
- Simplify:
[tex]\[
20x + 27x - 108 = 221
\][/tex]
2. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms on the left side:
[tex]\[
20x + 27x = 47x
\][/tex]
- This simplifies the equation to:
[tex]\[
47x - 108 = 221
\][/tex]
3. Isolate the variable ([tex]\( x \)[/tex]):
- Add 108 to both sides to get rid of the constant on the left:
[tex]\[
47x - 108 + 108 = 221 + 108
\][/tex]
- Simplify:
[tex]\[
47x = 329
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Divide both sides of the equation by 47 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{329}{47}
\][/tex]
- This gives:
[tex]\[
x = 7
\][/tex]
So, the solution to the equation is [tex]\( x = 7 \)[/tex].
